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Multi‐scale modelling of two‐phase–two‐component processes in heterogeneous porous media
Author(s) -
Niessner J.,
Helmig R.
Publication year - 2006
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.497
Subject(s) - porous medium , component (thermodynamics) , scale (ratio) , flow (mathematics) , domain (mathematical analysis) , work (physics) , phase (matter) , computer science , sink (geography) , porosity , mechanics , mathematics , geology , geotechnical engineering , physics , mathematical analysis , thermodynamics , cartography , quantum mechanics , geography
This work deals with flow and transport phenomena in porous media, which occur on different space and time scales. Additionally, the porous medium itself is heterogeneous where the heterogeneities occur on all spatial scales. We consider a large domain with randomly distributed heterogeneities where complex two‐phase–two‐component processes are relevant only in a small (local) subdomain. This subdomain needs fine resolution as the complex processes are governed by small‐scale effects. For a comprehensive fine‐scale model taking into account two‐phase–two‐component processes as well as heterogeneities in the whole (global) model domain, data collection is expensive and computational time is high. Therefore, we developed a multi‐scale concept where on the one hand, the global flow field influences the local two‐phase–two‐component processes on the fine scale. On the other hand, a coarse‐scale saturation equation is solved where the effects of the fine‐scale two‐phase–two‐component processes in the subdomain are captured by source/sink terms and the effects of fine‐scale heterogeneities by a macrodispersion term. Copyright © 2006 John Wiley & Sons, Ltd.